Anti-Affine Groups and Torsion Points
Amith Shastri K.Assistant Professor ,School of Arts and Sciences andSchool of Computing and Data ScienceAbout Author:Amith has 8 years of research experience in Mathematics and has worked across the domain including algebraic geometry and group theory. Amith has done PhD from TIFR, Mumbai. He has two publications, Character on a homogeneous space and Jacobians, anti-affine groups and torsion points.He began his career with TIFR as research scholar. Subsequently, he joined CMI in Siruseri as a postdoc before joining Sai University. While pursuing his Ph D, he has tutored in AFS and ATM schools and has taught undergraduates and graduate students during his postdoc at CMI.Abstract :We give a criterion for the Jacobian of a singular curve X with at most ordinary n-point singularities to be anti-affine. In particular, for the case of curves with single ordinary double point we exhibit a relation with torsion divisors. If the geometric genus of the singular curve is atleast 3 and the normalization is non-hyperelliptic and non-bielliptic, then except for finitely many cases the Jacobian of X is anti-affine. Furthermore, if the normalization is a general curve of genus atleast 3 then the Jacobian of X is always anti-affine.
